{
  "id": "2106.07844",
  "version": "v1",
  "published": "2021-06-15T02:34:28.000Z",
  "updated": "2021-06-15T02:34:28.000Z",
  "title": "The ultimate state of turbulent permeable-channel flow",
  "authors": [
    "Shingo Motoki",
    "Kentaro Tsugawa",
    "Masaki Shimizu",
    "Genta Kawahara"
  ],
  "comment": "10 pages, 5 figures",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "Direct numerical simulations have been performed for heat and momentum transfer in internally heated turbulent shear flow of constant bulk mean velocity and temperature, $u_{b}$ and $\\theta_{b}$, between parallel, isothermal, no-slip and permeable walls. The wall-normal transpiration} velocity on the walls $y=\\pm h$ is assumed to be proportional to the local pressure fluctuations, i.e. $v=\\pm \\beta p/\\rho$ (Jim\\'enez et al., J. Fluid Mech., vol. 442, 2001, pp.89-117). Here $\\rho$ is the mass density of the fluid, and the property of the permeable wall is given by the dimensionless parameter $\\beta u_{b}$. The temperature is supposed to be a passive scalar, and the Prandtl number is set to unity. In the permeable channel for $\\beta u_{b}=0.5$, we have found the critical transition of the scaling of the Stanton number St and the friction coefficient $c_{f}$ from the Blasius empirical law $St\\approx c_{f}\\sim Re_{b}^{-1/4}$ to the so-called ultimate state represented by $St\\sim Re_{b}^{0}$ and $c_{f}\\sim Re_{b}^{0}$ at the bulk Reynolds number $Re_{b}\\sim10^{4}$. The ultimate state is attributed to significant heat and momentum transfer enhancement without flow separation by intense large-scale spanwise rolls with the length scale of $O(h)$ arising from the Kelvin-Helmholtz instability over the permeable walls. The large-scale rolls can induce large-amplitude velocity fluctuations of $O(u_{b})$, so that the Taylor dissipation law $\\epsilon\\sim u_{b}^{3}/h$ (or equivalently $c_{f}\\sim Re_{b}^{0}$) holds, and similarly the temperature fluctuations of $O(\\theta_{b})$. As a consequence, the ultimate heat transfer is achieved, i.e., a wall heat flux scales with $u_{b}\\theta_{b}$ (or equivalently $St\\sim Re_{b}^{0}$) independent of thermal diffusivity, although the heat transfer on the walls is dominated by thermal conduction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-15T02:34:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ultimate state",
      "turbulent permeable-channel flow",
      "heated turbulent shear flow",
      "permeable wall",
      "momentum transfer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}